Study On Observer Based Adaptive Fuzzy Control

As an important branch in the field of intelligent control, fuzzy adaptive control for nonlinear systems has been received more and more attention in recent years. Some correlative issues in this area are studied in this paper. The main issues are the controller and observer design problems of uncertain nonlinear systems. The design and analysis procedure is based on a series of control theories, which include Lyapunov stability theory, input-to-state stability theory, small-gain theorem, adaptive control theory, fuzzy approximate theory, and so on. The main work in this paper is summarized as follows.Firstly, using H∞control technique and T-S fuzzy systems, an observer-based direct adaptive fuzzy control is developed for a class of uncertain nonlinear systems under the condition that not all of the state variables of the systems is available. By introducing the adaptive compensation term of the optimal approximation error, the square integrable condition of the approximation error is avoided. Based on Lyapunov stability theorem, the closed-loop adaptive fuzzy control system is proved to be semi-globally uniformly ultimately bounded, with the tracking error converging to zero asymptotically.Secondly, an observer-based direct adaptive fuzzy control is developed for a class of nonaffine uncertain nonlinear systems under the condition that not all of the state variables of the systems is available. Using Taylor expansion method and connotative function theorem, the controlled object is changed into a class of uncertain nonlinear systems with unknown gain function. The observer-based adaptive fuzzy controller is gained by use of H∞control technique and fuzzy systems. Not only the square integrable condition of the approximation error is avoided, but also the good tracking performance is obtained. Based on Lyapunov stability theorem, the closed-loop adaptive fuzzy control system is proved to be semi-globally uniformly ultimately bounded, with the tracking error converging to zero asymptotically.Thirdly, using ISS theory, small-gain theorem and T-S type fuzzy logic systems, which are used to approximate the uncertain system function, a Luenberger observer-based direct robust adaptive fuzzy control is developed for a class of nonlinear systems with unknown constant gain under the condition that not all of the state variables of the systems are available. The resulting closed-loop system is proved to be semi-globally uniformly ultimately bounded. In addition, the controller singularity problem commonly encountered in adaptive feedback linearization control can be avoided and only two learning parameters need to be adjusted on line.Lastly, using ISS theory, small-gain theorem and T-S type fuzzy logic systems, which are used to approximate the uncertain system function, a high-gain observer-based robust adaptive fuzzy control is developed for a class of nonlinear systems with uncertain gain function under the condition that not all of the state variables of the systems is available. The supposed condition that the unavailable state and the observed state of the systems have upper bounds usually encountered in adaptive fuzzy control which is based on common observer is avoided. The resulting closed-loop system is proved to be semi-globally uniformly ultimately bounded. In addition, the controller singularity problem commonly encountered in adaptive feedback linearization control can be avoided and only two learning parameters need to be adjusted on line. Simulation results show the effectiveness of the control scheme.Through the research in this paper, some fuzzy adaptive control problems for uncertain nonlinear systems have been properly solved. Numerical simulation experiments of these control schemes demonstrate their effectiveness.